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3 years ago

7

Use opposite operations to solve 3/4 x=6

1 answer:

borishaifa [10]3 years ago

4 0

Answer:

x=8

Step-by-step explanation:

3x/(4 x 4) =6(4)

cancel the four in the left side

3x=24

then divide 3 on both sides

3x/3=24/3

cancel the 3 on the left

x=8

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3 years ago

Find all points on the curve that have the given slope.x = 2cost, y= 8sint, slope =-1

tatuchka [14]

Answer:

$t_{1} = 0.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

$t_{2} = 1.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

Step-by-step explanation:

In the case of parametric equations, the slope of the curve is equal to:

$\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

Where $\frac{dx}{dt}$ and $\frac{dy}{dt}$ are the first derivatives of $x$ and $y$ regarding $t$ . Let be $x(t) =2\cdot \cos t$ and $y(t) = 8\cdot \sin t$ , their first derivatives are found:

$\frac{dx}{dt} = -2\cdot \sin t$ and $\frac{dy}{dt} = 8\cdot \cos t$

Thus, equation for the slope is:

$\frac{dy}{dx} = -\frac{8\cdot \cos t}{2\cdot \sin t}$

$\frac{dy}{dx} = -\frac{4}{\tan t}$

If $\frac{dy}{dx} = -1$ , then:

$-1 = -\frac{4}{\tan t}$

$\tan t = 4$

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$t_{1} = 0.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

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3 years ago

10500 people visited an art gallery in 2002.This was an increase of 25% on 2001.How many visitors were there in 2001?

Alenkasestr [34]

There were (10500/1.25) = 8400 visitors in 2001.

Explanation:
An increase of 25% means multiplying by 1.25. So, if the visitors from 2001 are multiplied by 1.25, then the result is 10500. Thus, the amount from 2001 was 10500/1.25=8400

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3 years ago

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